PARIS/NEW YORK, June 3 (Reuters) - France stepped up its protests to the United States on Tuesday over a possible $10 billion-plus sanctions busting fine for its biggest bank BNP Paribas, saying such a move could hurt transatlantic free-trade talks.

Foreign Minister Laurent Fabius' warning came two days before French President Francois Hollande hosts President Barack Obama for talks fraught with other sources of possible tension - from General Electric Co's overtures to emblematic French engineering group Alstom to differences over Syria and sanctions on Russia.

Until now, Hollande's senior ministers have shied away from commenting on BNP's negotiations with U.S. authorities, who are investigating whether the lender evaded U.S. sanctions relating primarily to Sudan, Iran and Syria between 2002 and 2009.

But Fabius, whose portfolio includes trade issues, noted the case came just as Washington and the European Union are negotiating a free-trade pact sought after by Obama, and that it would send the wrong signal if BNP's business was damaged.

"If there is an error or a violation then it's normal that there is a fine, but the fine has to be proportionate and reasonable," he told France 2 TV. Sources familiar with the discussions say the fine could be over $10 billion, which would nearly swallow up BNP's 2013 pretax income of 8.2 billion euros ($11.2 billion).

"Here you would have an example of an unfair and unilateral decision. It would be an extremely serious problem. You can't consider reciprocity to be the rule, when at the same time you have a decision like this," Fabius said.

"It's an extremely serious question that the Americans must handle in a spirit of partnership and not unilaterally."

Hollande himself has already expressed concern about BNP's case during a phone call to the White House more than two weeks ago, according to a person familiar with the matter.

U.S. officials said Obama did not plan to bring up BNP at a dinner he is due to have with Hollande on Thursday, and suggested he would deflect entreaties from Hollande. "It's certainly not something we would raise, given that it's a matter for DOJ to handle appropriately," one official said.

Last week, French banking regulator Edouard Fernandez-Bollo, and Christian Noyer, governor of the Bank of France, met with prosecutors and regulators in New York, according to people close to the negotiations.

Two other sources said the overtures were unlikely to impact the direction of the negotiations.

U.S. authorities, including New York state's top banking regulator, the Justice Department and the Manhattan District Attorney allege BNP stripped out identifying information from wire transfers so they could pass through the U.S. financial system without raising red flags, sources told Reuters.

The sources say any fine could be accompanied by potentially worse penalties, such as a possible temporary suspension of the bank's authority to clear U.S. dollar transactions.

Prosecutors have also insisted that the main listed bank plead guilty to the misconduct, but sources said BNP is pushing for one of its subsidiaries to take the hit of the plea. Negotiators are expected to iron out the details of the plea agreement in the next week, one source said.

BNP has said only that it is in discussions with U.S. authorities about "certain U.S. dollar payments involving countries, persons and entities that could have been subject to economic sanctions". It declined to comment on the matter on Tuesday. It has set aside $1.1 billion for the fine but told shareholders it could be far higher than that. Last month it also said it had improved control processes to ensure such mistakes did not occur again.

SYRIA, RUSSIA ANOTHER SOURCE OF TENSION

The intervention by Fabius, a veteran former prime minister not known for emotive language, underlines the growing concern in Paris that a fine of such magnitude could seriously damage BNP and have wider repercussions for the euro zone's second-largest economy, which flatlined in the first quarter.

French Finance Minister Michel Sapin added his concerns, telling Les Echos national newspaper that "France will react strongly to protect its fundamental interests" if U.S. authorities do not treat BNP fairly. "We are not here to defend a bank which has recognized wrongful acts. We are here to protect the stability of the financial system in France, to ensure its ability to finance the economy properly," he said.

The strong reaction from French officials could give a foretaste of the mood of Hollande's Paris dinner with Obama before the two head to Normandy the next day for the 70th anniversary of the D-Day landings that helped end World War Two.

At a joint news conference with his U.S. counterpart John Kerry in Washington last month, Fabius made clear that Paris was still unhappy with the Obama administration for its last-minute move in September 2013 to halt plans for joint military action in Syria - even as France readied its jets for take-off.

For its part, Washington has expressed its frustration at France's insistence on pursuing an existing contract to supply Mistral helicopters to Russia despite Western efforts to use sanctions to pressure Moscow over the Ukrainian stand-off.

The openly expressed preference of some of Hollande's team - notably the leftist Economy Minister Arnaud Montebourg - for a rival bid to thwart GE's efforts to buy Alstom's energy business will not improve the atmosphere on Thursday night.

Hollande's office said this week BNP would be raised in the talks alongside discussion of the crises in Ukraine and Syria, but has sought to play down sources of tension.

Hollande will go into the talks weakened both at home and beyond; his ruling Socialists were beaten badly in municipal elections in March over their failure to right the economy and again in last week's European Parliament elections, where the far-right National Front came first in France.

The National Front last week demanded his government stop "twiddling its thumbs" over BNP and stand up for French interests in what it called a U.S. "racket."

Warning of possible consequences for the U.S.-European trade pact could be one way for Paris to try and influence the BNP outcome - any pact must be approved by its parliament and other national assemblies in the 28 members of the European Union. ($1 = 0.7349 Euros) (Additional reporting by Emmanuel Jarry, Maya Nikolaeva, Aruna Viswanatha and Jeff Mason; Writing by Mark John and Andrew Callus; Editing by Will Waterman and Lisa Shumaker)